کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1149396 957877 2010 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Rate of uniform consistency for nonparametric estimates with functional variables
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Rate of uniform consistency for nonparametric estimates with functional variables
چکیده انگلیسی

In this paper we investigate nonparametric estimation of some functionals of the conditional distribution of a scalar response variable Y given a random variable X taking values in a semi-metric space. These functionals include the regression function, the conditional cumulative distribution, the conditional density and some other ones. The literature on nonparametric functional statistics is only concerning pointwise consistency results, and our main aim is to prove the uniform almost complete convergence (with rate) of the kernel estimators of these nonparametric models. Unlike in standard multivariate cases, the gap between pointwise and uniform results is not immediate. So, suitable topological considerations are needed, implying changes in the rates of convergence which are quantified by entropy considerations. These theoretical uniform consistency results are (or will be) key tools for many further developments in functional data analysis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 140, Issue 2, February 2010, Pages 335–352
نویسندگان
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